Question

I’m doing Project Euler #19. It’s obviously a trivial problem if you just want to loop through month-by month and apply some high-school modular arithmetic but I’m trying a different approach just for fun.

I note that Jan/Feb 1 1901 are not Sundays, neither are Jan/Feb 1 2001, hence I can view my calendar year as starting on March 1. Using basic modular arithmetic, it’s easily seen that if leap years didn’t exist, then the number of Xdays in a given year is a repeating sequence {2,2,2,1,2,1,2} since 365 is congruent 1 (mod 7). So factoring a leap year results in a a 2 element jump in the sequence. So I’ve written this code to complete the problem:

const unsigned s[7] = {2,2,2,1,2,1,2};
unsigned n = 0;  
unsigned y = 1901;
unsigned c = 0;
do {
    c=c%7;
    n+=s[c];
    ++y; 
    c += ((y%4!=0)||(y%400==0) ? 1 : 2); 
} while (y<2001);
std::cout << n << std::endl;

However I’m getting 172 where the answer is 171. Anyone see where I’ve gone wrong?

Note: please don’t leave 1200/7 comments.

FIXED: replacing with c += ((y%400==0)||((y%4==0)&&(y%100!=0)) ? 2 : 1);

Answer 1

edit: about the leap-year rule.

The leap year rule has just one more special case.

A year is a leap year if it is:

• Divisible by four
  • But not divisible by 100
    • Except when it is also divisible by 400

Sometimes I wish we had metric calendars. Megaseconds and kiloseconds, anybody?

---

Maybe you got a bit confused about the leap-year rule?

From your link:

A leap year occurs on any year evenly divisible by 4, but not on a century unless it is divisible by 400.

So a year divisible by 400 is a leap year. Your condition in your code is reversed.